Explanation of the Pigeon-Hole Principle

A detailed tutorial on the pigeon-hole principle. Step by step tutorial including several examples of the pigeon-hole principle for reference.

The pigeon-hole principle is an important principle in math that states that if n items are to be put into m pigeon-holes, and n > m, then at least one pigeon-hole must contain more than one item. It is thought of as an extension of the counting principle. The pigeon-hole principle was first referred to as the drawer principle, or the shelf principle. Because of this, it is commonly called Dirichlet’s box principle or Dirichlet’s drawer principle. It is most commonly used with finite sets of elements; however, this principle can also be used with infinite sets.